Revision as of 00:39, 22 December 2017

Glider synthesis (or glider construction) is the construction of an object by means of glider collisions. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement.

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Features of syntheses

Four main characterizing features of a synthesis are the geometry, reaction speed, reaction multiplicity, and glider cost.

The geometry is the number of directions of incoming gliders:

four-directional: gliders collide from all four directions

three-directional: gliders collide from all directions but one

two-directional; further divisible in head-on and 90° syntheses. All two-glider syntheses are necessarily two-directional.

unidirectional, which assumes the initial presence of a target (usually a still life or an oscillator) to be hit with gliders.

Since gliders are themselves glider-constructible, any multidirectional synthesis can be technically downgraded to a fewer-directional one, usually at the cost of increasing the speed, multiplicity and cost of the synthesis. More challenging is finding a two- or three-directional synthesis for a particular object where few or no parts of the synthesis reactions extend outside the final pattern's bounding box in a particular direction. This is especially important for the synthesis of temporary catalysts, which will need to be placed sometimes quite close to other components without perturbing them. For especially tight locations, sometimes it will be useful to construct an LWSS (or another standard c/2 spaceship) some ways away from the synthesis nexus and let that collide with a glider in the final stages; this allows synthesis at a 45° angle, rather than a 90° angle as required for synthesis by gliders from separate directions.

The speed is simply the number of generations it takes to complete a synthesis. For multi-stage syntheses, each stage has its own speed.

The multiplicity is the number of stages a synthesis operates in. Often a particular synthesis operation cannot be achieved by a direct collision of gliders, and a synthesis procedure instead requires first synthesizing a number of catalysts, and then hitting these with gliders to produce the final result.

The cost is the number of gliders expended over the course of the synthesis. Much as speed, it can be defined also for individual synthesis stages.

Of particular interest is slow salvo synthesis: unidirectional synthesis where every stage has a glider cost of one. Perhaps surprisingly, anything that is glider synthesizable is also slow salvo synthesizable; a result that crucially depends on the existence of movable targets and splitters.

Syntheses of note

A 3-glider synthesis of a pentadecathlon was found in April 1997 by Heinrich Koenig, which came as a surprise because it was widely assumed that anything using just three gliders would already be known.

Spaceship syntheses

Perhaps the most interesting glider syntheses are those of spaceships, because these can be used to create corresponding guns and rakes. Many of the c/2 spaceships that are based on standard spaceships have been synthesized, mostly by Mark Niemiec. In June 1998, Stephen Silver found syntheses for some of the Corderships (although it was not until July 1999 that Jason Summers used this to build a Cordership gun). In May 2000, Noam Elkies suggested that a 2c/5 spaceship (60P5H2V0) found by Tim Coe in May 1996 might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March 2003 that Summers and Elkies managed to find a way to perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in Life of a rake which fires spaceships that travel in the same direction as the rake but more slowly.

After the loafer was discovered and synthesized in 2013, a number of new spaceship syntheses were found during a short period of time in late 2014 and early 2015, including the dart, crab, 25P3H1V0.2, 30P5H2V0, x66, and weekender. Most of this was due to the work of Martin Grant.